2. Show, using the per capita production function, that z,= (k,/A,) ' - ".Then show, by writing this equation for period t + 1, using the definition k,. 1 "' K,. ,I L ,. ,. and then using the model's equations, that:

From this equation show by appropriate manipulations that the law of motion for z, is:

(5 1)

(Hint: Start by taking k, out of the middle parentheses and then utilize the fact that inside the parentheses you get y,/k,= 1/ z,, and outside you get a k:-" that you can put together with the (1 /A 1

) , _,to make z, appear).